We theoretically explore possible unconventional superconductivity induced by
weak repulsive interactions in twisted bilayer TMD (e.g. WSe2​) in the
presence of an out-of-plane electric field. Using renormalization group (RG)
analysis, we show that topological chiral superconducting states with Chern
number N=1,2,4 (namely p+ip, d+id, g+ig) appear over a large
parameter region with moire filling factor around n=1. At some special values
of applied electric field and in the presence of a weak out-of-plane Zeeman
field, spin-polarized pair density wave (PDW) superconductivity can emerge.
This spin-polarized PDW state can be probed by experiments such as
spin-polarized STM measuring spin-resolved pairing gap and quasi-particle
interference. Moreover, the spin-polarized PDW could lead to spin-polarized
superconducting diode effect.Comment: 5 pages and 4 figs with supplementary materia